This invention relates to a method and apparatus for determining the relative height of two targets.
The need to determine the relative height of two points is common in construction, surveying, and navigation. (Relative height, in the present contexts, is always measured with respect to the direction of gravity.) This need is most commonly met by placing an observer either at one of the points or on a line between the two points. In many situations this is impractical or undesirable, since the observer wishes to perform the measurement at a location which is remote to the points.
From a remote location the measurement is most commonly performed using a leveled table called an alidade, from which angular measurements may be made to the two points. According to the tenets of Euclidean geometry, the relative height of the two points may be determined by triangulation using single measurements (often in conjunction with at least one known distance); and this historically has been the accepted method in use.
However, it is often easier to measure distance accurately rather than angular displacement owing to the proliferation of technologies that allow precision distance measurements (e.g. microwave, acoustic, laser, etc.). Distance measuring may be accomplished by measuring the signal propagation time from a transmitter to a receiver. Often the transmitter and receiver are incorporated into the same apparatus, and placed in juxtaposition to a remote signal-reflecting target. Using the signal-reflecting target, the distance to be measured is traversed by the signal from the apparatus to the target and again from the target back to the apparatus, imposing a nominal distance correction calculation. With more sophisticated apparatus, a first signal is sent from the apparatus to the target; and the target actively responds to the first signal by sending back a second signal.
For modest domestic distances (e.g. less than 1000 meters) the first signal may be a radio signal whose distance traversal time may be neglected; and the second signal may be an acoustic signal whose distance traversal time may be very accurately and easily measured. This use of a radio signal trigger for an acoustic signal response is ideal for distance measuring applications; firstly because both signals may be sent Omni-directionally; and secondly because, when a plurality of targets are used, the targets may be individually addressed by coding the radio signal.
Various approaches to the determination of relative height are described in the patent literature. For example, U.S. Pat. Nos. 4,685,219 and 5,209,449 show the use of spirit levels. U.S. Pat. Nos. 4,356,639 5,010,768; 5,307,698 and 5,617,640 disclose the use of fluid filled tubes for leveling. Other leveling techniques are described in U.S. Pat. No. 4,069,591 which describes the use of a pendulum for leveling; and in U.S. Pat. No. 4,561,188 wherein the use of a gyroscope for leveling is disclosed. U.S. Pat. Nos. 4,673,287 and 5,189,484 show the use of lasers for leveling; whilst U.S. Pat. No. 5,075,772 employs a video camera for the same purpose.
Likewise, various approaches to precise distance measurement are described in U.S. Pat. Nos. 4,498,764 and 4,498,764 that employ optical techniques; and in U.S. Pat. Nos. 4,820,041; 4,911,548 and 5,592,401 that measure distance based on position coordinates.
All of the prior art approaches either improve a constraint on the location of the observer or require angular measurement, both of which are inconvenient.
It is therefore an object of the present invention to allow for the relative height between two points both of of which are remote from the location of measurement to determined using precise distance measurements.
In accordance with a broad aspect of the invention there is provided a method for determining the relative height between two points, the method comprising the steps of:
(a) placing a first signal-responsive target-object (hereinafter xe2x80x9ctargetxe2x80x9d) on the first point and placing a second signal-responsive target-object (hereinafter xe2x80x9ctargetxe2x80x9d) on the second point,
(b) signaling each of the targets from a first reference which is remove from both targets and measuring a respective first and second distance from the first reference to the two targets,
(c) signaling each of the targets from a second reference which is displaced a known distance and angular orientation from the first reference and which is remote from both targets and measuring a respective third and fourth distance from the second reference to the two targets,
(d) determining a first triangle formed by the first and second reference points and a first one of the two targets,
(c) determining a second triangle formed by the first and second reference points and a second one of the two targets, and
(f) forming a virtual tetrahedron from the first and second triangles and calculating the relative height between the two targets (the target-to-target edge of the tetrahedron).
It is thus to be understood that such a method requires no angular measurements in order to determine the differential height between the two targets (when the first and second reference are substantially aligned vertically), but rather only distance measurements which can be performed simply and accurately. Furthermore, only nominal corrections (calculations) are required when the reference are not substantially aligned vertically with respect to each other. These nominal corrections are enhanced when the angular displacement of the two references (with respect to the direction of gravity) is known, otherwise the corrections substantially relate to margins of error.
Preferably the first and second reference points are displaced vertically a known distance from one another in order to simplify the trigonometry. Such a method imposes no constrain on the location of an observer and thus allows convenient measurement of locations (targets) that are remote from the observer and not easily accessible.
An apparatus for carrying out such a method comprises:
two (or more) signal-responsive target-objects (for use pair-wise);
a casing housing first and second measurement ports displaced a known distance from each other;
at least one signaling module within the casing at each of the measurement ports being sufficient for signaling each of the two targets from both of the measurement ports,
a distance measuring module coupled to each of the signaling modules for measuring the distance from each port to each target according to the responsive signalings of the corresponding signaling modules; and
a calculation module coupled to the signaling modules and to the distance measuring modules and being responsive to the measured distances for determining:
(a) a first triangle formed by the first and second measurement ports and a first one of the two targets,
(b) a second triangle formed by the first and second measurement ports and a second one of the two targets, and
(c) the relative height between the two targets (with respect to each other) as the height of a virtual tetrahedron formed from the first and second triangles.
According to the preferred embodiment of the apparatus of the present invention, each target is uniquely addressable by the signaling (as described in the background section using the example of xe2x80x9ccoding the radio signalxe2x80x9d).
In use the apparatus may be mounted on a tripod including a leveling device for ensuring that the two measurement ports are displaced exactly vertically. Preferably, a display device is coupled to the calculation module so as to provide an immediate readout of the measured relative height. However, the result can be stored for subsequent downloading to a computer or other external system, if required. This use of storage and downloading is especially useful when pair-wise measuring the relative heights of a plurality of target objects.